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Incorporating graphical structure of Predictors in Sparse Quantile Regression

JOURNAL OF BUSINESS & ECONOMIC STATISTICS 2021年第3期39卷 783-792页

作者： Wang, Zhanfeng Liu, Xianhui Tang, Wenlu Lin, Yuanyuan Univ Sci & Technol China Sch Management Int Inst Finance Hefei Peoples R China Jiangxi Univ Finance & Econ Sch Stat Nanchang Jiangxi Peoples R China Jiangxi Univ Finance & Econ Res Ctr Appl Stat Nanchang Jiangxi Peoples R China Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China

Quantile regression in high-dimensional settings is useful in analyzing high-dimensional heterogeneous data. In this article, different from existing methods in quantile regression which treat all the predictors equally with the same priori, we take advantage of the graphical structure among predictors to improve the performance of parameter estimation, model selection, and prediction in sparse quantile regression. It is shown under mild conditions that the proposed method enjoys the model selection consistency and the oracle properties. An alternating direction method of multipliers algorithm with a linearization technique is proposed to implement the proposed method numerically, and its convergence is justified. Simulation studies are conducted, showing that the proposed method is superior to existing methods in terms of estimation accuracy and predictive power. The proposed method is also applied to a real dataset.

关键词： ADMM algorithm graphical structure Quantile regression Sparse regression

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High-dimensional generalized linear models incorporating graphical structure among predictors

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ELECTRONIC JOURNAL OF STATISTICS 2019年第2期13卷 3161-3194页

作者： Zhou, Shengbin Zhou, Jingke Zhang, Bo Lingnan Normal Univ Coll Informat Engn Zhanjiang 524048 Peoples R China Southwestern Univ Finance & Econ Sch Stat Chengdu Sichuan Peoples R China Renmin Univ China Sch Stat Beijing Peoples R China

In this paper, we propose a sparse generalized linear model incorporating graphical structure among predictors (sGLMg), which is an extension of [37] where they exploit the structure information among predictors to improve the performance for the linear regression. There is an explicit expression between the coefficient and the predictor graph measured by the precision matrix in the linear regression, however, this structure does not exist in generalized linear model for the explicit expression of the coefficient in generalized linear model is usually hard to be obtained. To incorporate the graphical structure among predictors for generalized linear models, we make use of the sufficient reduction techniques to reestablish the relationship between the coefficient and the precision matrix. The oracle inequalities of the estimator for sGLMg are also presented and the finite sample performance of the proposed methods is examined via numerical simulations and a breast cancer data analysis.

关键词： graphical structure sparse regression generalized linear models sufficient dimension reduction oracle inequalities

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High-dimensional expectile regression incorporating graphical structure among predictors

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2023年第2期93卷 231-248页

作者： Pan, Yingli Zhao, Xiaoluo Wei, Sha Liu, Zhan Hubei Univ Fac Math & Stat Hubei Key Lab Appl Math Wuhan 430062 Peoples R China

With the extensive application of high-dimensional heterogeneous data in various disciplines, sparse expectile regression is increasingly favoured by people. In this paper, we make use of the graphical structure among predictors node-by-node to improve the performance of parameter estimation, model selection and prediction in sparse expectile regression. A modified alternating direction method of multipliers (ADMM) algorithm with a linearization trick is proposed to implement the proposed method numerically, and the convergence of the algorithm is proved. Simulation studies are conducted to evaluate the finite-sample performance of the proposed method. We demonstrate the practicability of the proposed approach with a dataset of the expression quantitative trait locus mapping (eQTL) experiment in Rattus norvegicus.

关键词： Heterogeneous data sparse expectile regression graphical structure modified ADMM algorithm

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Tree-Connectivity: Evaluating the graphical structure of SLAM

Tree-Connectivity: Evaluating the Graphical Structure of SLA...

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IEEE International Conference on Robotics and Automation

作者： Kasra Khosoussi Shoudong Huang Gamini Dissanayake the Centre for Autonomous Systems (CAS) Faculty of Engineering and Information Technology University of Technology Sydney Australia

ISBN: (纸本)9781467380270

Simultaneous localization and mapping (SLAM) in robotics, and a number of related problems that arise in sensor networks are instances of estimation problems over weighted graphs. This paper studies the relation between the graphical representation of such problems and estimation-theoretic concepts such as the Cramér-Rao lower bound (CRLB) and D-optimality. We prove that the weighted number of spanning trees, as a graph connectivity metric, is closely related to the determinant of CRLB. This metric can be efficiently computed for large graphs by exploiting the sparse structure of underlying estimation problems. Our analysis is validated using experiments with publicly available pose-graph SLAM datasets.

关键词： Evaluating graphical structure SLAM

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GUNet: A GCN-CNN Hybrid Model for Retinal Vessel Segmentation by Learning graphical structures 1

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9th International Workshop on Ophthalmic Medical Image Analysis (OMIA)

作者： Zhang, Yishuo Chung, Albert C. S. Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Sai Kung Hong Kong Peoples R China

ISBN: (数字)9783031165252

ISBN: (纸本)9783031165252;9783031165245

In the retinal vessel segmentation task, maintaining graphical structures of vessels is important for the following analysis steps. However, this task is challenging due to the tiny structures of vessels and bad image quality. Existing methods based on Convolutional Neural Networks (CNNs) can capture local appearances from the regular image grid but are limited to learning high-level features from graphical structures. Motivated by Graph Convolution Networks (GCNs) which capture information on graphs, we propose a novel GCN-CNN hybrid U-shaped model, namely GUNet, which is capable of extracting graphical information of vessels. The hybrid model inherits both merits of CNNs and GCNs. The convolutional blocks extract basic feature representations from local appearances while the GCN blocks learn high-level long-range graphical features along vessels at a deep level. To obtain graphs which effectively represent vessels, we constructed graphs based on the preliminary vessel skeleton segmentation followed by a Hessian filter for vessel enhancement. GUNet takes raw images and corresponding graphs as input and can be trained in an end-to-end manner. The proposed method is evaluated on two fundus photography datasets (STARE and CHASE) and one Scanning Laser Ophthalmoscopy (SLO) dataset (IOSTAR). We conduct experiments to demonstrate that the GCNs module brings significant benefits in terms of graphical similarity and further leads to better overall performances. GUNet also achieves competitive performances compared with state-of-the-art methods.

关键词： Retinal vessel segmentation Convolutional Neural Networks Graph Convolutional Networks graphical structure

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Multivariate sparse Laplacian shrinkage for joint estimation of two graphical structures

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2023年 178卷

作者： Yang, Yuehan Xia, Siwei Yang, Hu Cent Univ Finance & Econ Sch Stat & Math Beijing Peoples R China Civil Aviat Flight Univ China Sch Sci Deyang Peoples R China Chongqing Univ Coll Math & Stat Chongqing Peoples R China

Multivariate regression models are widely used in various fields for fitting multiple responses. In this paper, we proposed a sparse Laplacian shrinkage estimator for the high -dimensional multivariate regression models. We consider two graphical structures among predictors and responses. The proposed method explores the regression relationship allowing the predictors and responses derived from different multivariate normal distributions with general covariance matrices. In practice, the correlations within data are often complex and interact with each other based on the regression function. The proposed method solves this problem by building a structured penalty to encourage the shared structure between the graphs and the regression coefficients. We provide theoretical results under reasonable conditions and discuss the related algorithm. The effectiveness of the proposed method is demonstrated in a variety of simulations as well as an application to the index tracking problem in the stock market. (C) 2022 Elsevier B.V. All rights reserved.

关键词： graphical structure High -dimensional data Laplacian smoothness Multivariate regression

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Improved Bonferroni mean operator to apprehend graph based data interconnections with application to the Hacker Attack system

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INFORMATION SCIENCES 2022年 616卷 276-302页

作者： Hait, Swati Rani Dutta, Bapi Guha, Debashree Chakraborty, Debjani Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India Univ Jaen Dept Comp Sci Jaen 23071 Spain Indian Inst Technol Kharagpur Sch Med Sci & Technol Kharagpur 721302 W Bengal India

The Bonferroni mean (BM) operator has extended the class of interrelationship handling fusion functions by modeling homogeneous pairwise interactions among data entities. This operator has been further extended to diverse directions with the intention of capturing dissimilar association that exists within data sets of different real-world systems like, social network systems, biological systems, etc. It has been observed that some of the existing forms of the BM operator pre-assumes a specific model of association among data entities during its formulation, which may not be feasible in many systems. In this study, an effort has been made to develop the framework of the BM operator by generalizing the structure of relationship patterns among data entities. Classical graphs are considered as a prominent tool for describing pairwise relations among data entities. Such consideration prompted the proposal of a systematized framework of an improved version of the BM operator, denoted by the f BM G operator, where the unconventional association among data entities are portrayed through different graphical patterns. The f BM G operator has been formulated in a way that the knowledge of interactional information depicted through graphs is embedded into its processing system with the aim of capturing precise interconnections among entities. The generalized variation of the f BM G operator has also been proposed by substituting the sub-components of the f BM G operator with other precise forms of the aggregation functions to provide an illustrative alignment, which is quite expressible and interpretable, and also facilitates modeling mandatory prerequisites of the decision systems. For an applicatory aspect, the proposed operators have been utilized over the Hacker attack system and have been presented with a numerical example. A detailed comprehensive analysis has been presented to demonstrate the efficiency of the proposed operators. (c) 2022 Elsevier Inc. All rights reserve

关键词： graphical structure Aggregation operators Bonferroni mean Improved Bonferroni mean operator Generalized Bonferroni mean operator Hacker attack system

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Structural Complexity of One-Dimensional Random Geometric Graphs

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第2期69卷 794-812页

作者： Badiu, Mihai-Alin Coon, Justin P. Univ Oxford Dept Engn Sci Oxford OX1 3PJ England

We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by n nodes randomly scattered in [0, 1] that connect if they are within the connection range r is an element of [0, 1]. We provide bounds on the number of possible structures which give universal upper bounds on the structural entropy that hold for any n, r and distribution of the node locations. For fixed r, the number of structures is Theta(a(2n)) with a = a(r) = 2cos (pi/ 1/r +2 ), and therefore the structural entropy is upper bounded by 2n log(2) a(r)+ O(1). For large n, we derive bounds on the structural entropy normalized by n, and evaluate them for independent and uniformly distributed node locations. When the connection range r(n) is O(1/n), the obtained upper bound is given in terms of a function that increases with nr(n) and asymptotically attains 2 bits per node. If the connection range is bounded away from zero and one, the upper and lower bounds decrease linearly with r, as 2(1- r) and (1- r) log(2) e, respectively. When rn is vanishing but dominates 1/n (e.g., r(n) alpha ln n/n), the normalized entropy is between log(2) e approximate to 1.44 and 2 bits per node. We also give a simple encoding scheme for random structures that requires 2 bits per node. The upper bounds in this paper easily extend to the entropy of the labeled random graph model, since this is given by the structural entropy plus a term that accounts for all the permutations of node labels that are possible for a given structure, which is no larger than log (2)(n!) = n log(2) n-n + O(log(2) n).

关键词： Entropy Complexity theory Upper bound Computational modeling Data models Channel coding Biological system modeling Random geometric graph entropy graphical structure graph isomorphism maximal cliques graph compression

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THE SPARSE LAPLACIAN SHRINKAGE ESTIMATOR FOR HIGH-DIMENSIONAL REGRESSION

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ANNALS OF STATISTICS 2011年第4期39卷 2021-2046页

作者： Huang, Jian Ma, Shuangge Li, Hongzhe Zhang, Cun-Hui Univ Iowa Dept Stat & Actuarial Sci Iowa City IA 52242 USA Yale Univ Sch Publ Hlth Div Biostat New Haven CT 06520 USA Univ Penn Sch Med Dept Biostat & Epidemiol Philadelphia PA 19104 USA Rutgers State Univ Dept Stat & Biostat Piscataway NJ 08854 USA

We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic associated with a graph as the penalty function. We call it the sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave penalty for encouraging sparsity and Laplacian quadratic penalty for promoting smoothness among coefficients associated with the correlated predictors. The SLS has a generalized grouping property with respect to the graph represented by the Laplacian quadratic. We show that the SLS possesses an oracle property in the sense that it is selection consistent and equal to the oracle Laplacian shrinkage estimator with high probability. This result holds in sparse, high-dimensional settings with p >> n under reasonable conditions. We derive a coordinate descent algorithm for computing the SLS estimates. Simulation studies are conducted to evaluate the performance of the SLS method and a real data example is used to illustrate its application.

关键词： graphical structure minimax concave penalty penalized regression high-dimensional data variable selection oracle property

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Edgewise and subgraph-level tests for brain networks

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STATISTICS IN MEDICINE 2016年第27期35卷 4994-5008页

作者： Chen, Huaihou Zhao, Bingxin Porges, Eric C. Cohen, Ronald A. Ebner, Natalie C. Univ Florida Dept Biostat Gainesville FL 32611 USA Univ Florida Inst Aging McKnight Brain Inst Ctr Cognit Aging & Memory CAMDept Aging Geriatr Gainesville FL USA Univ Florida Dept Psychol Gainesville FL 32611 USA

Resting-state functional magnetic resonance image is a useful technique for investigating brain functional connectivity at rest. In this work, we develop flexible regression models and methods for determining differences in resting-state functional connectivity as a function of age, gender, drug intervention, or neuropsychiatric disorders. We propose two complementary methods for identifying changes of edges and subgraphs. (i) For detecting changes of edges, we select the optimal model at each edge and then conduct contrast tests to identify the effects of the important variables while controlling the familywise error rate. (ii) We adopt the network-based statistics method to improve power by incorporating the graph topological structure. Both methods have wide applications for low signal-to-noise ratio data. We propose stability criteria for the choice of threshold in the network-based statistics procedure and utilize efficient massive parallel procedure to speed up the estimation and inference procedure. Results from our simulation studies show that the thresholds chosen by the proposed stability criteria outperform the Bonferroni threshold. To demonstrate applicability, we use both methods in the context of the Oxytocin and Aging Study to determine effects of age, gender, and drug treatment on resting-state functional connectivity, as well as in the context of the Autism Brain Imaging Data Exchange Study to determine effects of autism spectrum disorder on functional connectivity at rest. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： network-based statistics graphical structure resting-state brain functional connectivity

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